The terms $140, a, \frac{45}{28}$ are the first, second and third terms, respectively, of a geometric sequence. If $a$ is positive, what is the value of $a$?
Let the common ratio of the geometric sequence be $r$. We have the equations $140\cdot r = a$ and $a \cdot r = \frac{45}{28}$. In the first equation, we solve for $r$ to get $r=\frac{a}{140}$, and substitute this into the second equation to eliminate $r$, resulting in $a \cdot \frac{a}{140} = \frac{45}{28}$, or $a = \boxed{15}$.